Quantum Mechanical Model of the Atom

1
Quantum Mechanical Model of the Atom
2

• Many scientists contributed to the development of
  the quantum mechanical model of the atom.
• Bohr
• Planck
• DeBroglie
• Heisenberg
• Schrodinger
• Pauli

3
What was already known..

• Early 1900sbelieved that
• Energy is quantized
• Electrons have both wave and matter properties
• Electrons can be at a variety of specific energy
  levels in an atom
• Energy levels are called orbits (Bohr model)
• Proposed that electron had both wave and matter
  properties

4
Next round of research

• Goal was to describe electrons in atoms
• Ultimately describe for each electron
• Energy level size of the region it occupies (n)
  
• 3-D shape of the region it occupies (l)
• Orientation of the region/orbital (ml)
• Spin on the electron (ms)

5
Schrodinger deBroglie

• S deB pictured the electron bound to the atom
  in a standing wave
• Standing vs. traveling waves
• See page 253

6
Schrodinger

• Sch.. Proposed that electrons move around the
  nucleus in standing waves
• Each orbit represents some whole number multiple
  of a wavelength
• Schrodinger analyzed the hydrogen data based on
  the assumption that the electrons behaved as
  standing waves.

7
Schrodinger

• Schrodingers equation takes into account
• The position of the electron in 3D space (its
  x,y,z coordinates)
• Potential energy of the atom due to the
  attraction between electrons and protons
• Kinetic energy of the electron

8
Schrodinger

• Schrodingers equation has many solutions
• Each solution is called a wave function (y) and
  is correlated to a specific amount of energy
• Each wave function is more commonly called an
  orbital.

9
Orbitals

• Each solution to Schrodingers equation describes
  a specific wave function (y) /orbital
• The square of a wave function, (y)2, generates a
  probability distribution for an electron in that
  orbital
• Also called an electron density map for a given
  orbital
• (y)2 describes the shape, size, and orientation
  of the orbital

10
Orbitals

• Orbitals are regions in space where an electron
  is likely to be found
• 90 of the time the electron is within the
  boundaries described by the electron density map
• Can describe its energy, shape, and orientation
• The exact path of an electron in a given orbital
  is not known!

11
Heisenberg

• Heisenberg uncertainty principle states that we
  cannot know both the position and the momentum of
  an electron at the same time.
• Therefore, we do not know the exact path of the
  electron in an orbital.

12
Orbitals

• The lowest energy solution to Sch..s equation
  for an electron in a hydrogen atom describes what
  is known as the 1s orbital.
• See pages 306/307

13
Describing Orbitals

• Use quantum numbers to describe orbitals. A
  given orbital can be described by a set of 3
  quantum numbers
• Principal quantum number (n)
• Angular momentum quantum number (l)
• Magnetic quantum number (ml)

14
Principal Quantum Number (n)

• (n) describes the size and energy of the oribital
• Possible values whole number integer
• 1, 2, 3,
• As n increases so does the size and energy of
  the orbital

15
Angular momentum quantum number (l)

• (l) is related to the shape of the orbital
• Possible values (l) is an integer between 0 and
  n-1
• Each (l) value is also assigned a letter
  designation

16
Angular momentum quantum number (l)
(l) Value Letter Designation
0 s
1 p
2 d
3 f
17
n Possible l values Designation
1 0 1s
2 0 1 2s 2p
3 0 1 2 3s 3p 3d
4 0 1 2 3 4s 4p 4d 4f
18
Magnetic quantum number (ml)

• (ml) is related to the orientation of the orbital
  in 3-D space
• Possible values - l to l

19
Magnetic quantum number (ml)

• Consider the p orbitalit has an l value of 1 and
  thus the possible ml values are -1, 0, 1
• These 3 ml values correspond to the 3 possible
  orientations of the p orbital

20
Ml and Orbitals
l ml orbitals
0 (s) 0 1
1 (p) -1, 0, 1 3
2 (d) -2, -1, 0, 1, 2 5
3 (f) -3, -2, -1, 0, 1, 2, 3 7
21
Quantum Number Summary

• See page 256 and board.
• A set of 3 quantum numbers describes a specific
  orbital
• Energy and size - n
• Shape - l
• Orientation ml

22
4th Quantum Number!

• A 4th quantum number was added to describe the
  spin on a given electron.
• Called the electron spin quantum number - ms
• Possible values 1/2 and -1/2

23
More on electron spin.

• Each orbital can hold a maximum of 2 electrons of
  opposite spin.
• Pauli exclusion principle states that no two
  electrons in an atom can have the same set of 4
  quantum numbers

24
Summary

• Three quantum numbers describe a specific orbital
• Energy and size, shape, and orientation
• Four quantum numbers describe a specific electron
  in an atom

25
7.9 Polyelectronic atoms

• The Schrodinger model was based on H and works in
  principle for atoms with more than one electron.
• The shapes and possible orientations of the
  hydrogen based orbitals holds true for
  polyelectronic atoms.
• However, the size and energy of the orbitals in
  polyelectronic atoms differ from those calculated
  for hydrogen.

26
Polyelectronic Atoms

• In general, find that in a given principal
  quantum number (n)
• S is lower energy than p, which is lower energy
  than d..
• s lt p lt d lt f
• Already know that 1s lt 2s lt 3s and 2p lt 3p lt
  4p. (in terms of size and energy)

27
7.11 The Aufbau Principle

• Putting electrons in to orbitals
• Aufbau means building up in German
• Electrons always enter the lowest energy orbital
  with room

28
Hunds Rule

• The orbitals of a given sublevel (e.g. p, or d,
  or f) are degenerate (of the same energy).
• The lowest energy state occurs with the maximum
  number of unpaired electrons.
• Meaning..electrons enter an empty orbital of a
  given sublevel before pairing up.

29
Goals

• To be able to write for any atom
• Electron configuration
• Box/energy diagram
• Lewis dot symbol
• State the quantum numbers for each electron in an
  atom.
• To relate the electron configuration of an atom
  to its location on the periodic table and its
  properties.

30
Goals Elaborated

• Electron configuration shows the number of
  electrons in each sublevel
• Format 1s22s22p4 or He 2s22p4
• Box/energy diagram shows electrons as arrows
  and each orbital as a box. Electrons of opposite
  spin are indicated by up and down arrows.
• Format

31
Periodic Table and Electron Configurations
32
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s
33
Goals Elaborated

• Lewis Dot Symbol shows valence electrons as
  dots around the symbol for the atom
• Maximum of 2 electrons per side of the symbol
• Valence electrons are all of the electrons in the
  highest occupied principle quantum level (n)
• Format

34
The fun part - practice!

• Representative elements IA 8A
• Ions formed by above
• Transition metals
• Iron
• Ion formation
• Exceptions
• Cr expect ___ electrons in 3d
• Actually..
• Cu expect ___ electrons in 3d
• Actually..

35
CH 7 Atomic Structure and Periodicity

• Sections 7.10 -7.13

36
Periodic Trends

• Models explain observed behavior.
• The better the model the fewer the exceptions
• Consider computer weather models vs. kinetic
  molecular theory

37
Periodic Trends

• The quantum mechanical model of the atom explains
  many trends in the properties observed for the
  elements.
• Trends in physical properties
• Atomic radius
• Size of the ion vs. the parent atom
• Trends in reactivity
• Charge on the ion formed
• Ease of removing or adding an electron to an atom

38
Atomic Radius

• Measuring/defining atomic radius
• Metals atomic radius is half the distance
  between nuclei in a solid
• Nonmetals atomic radius is half the distance
  between the nuclei of atoms in a diatomic molecule

Cu
H
H
39
Atomic radius trends (pg 276)

• Atomic radius increases down a group
• Valence electrons are in higher (larger)
  principal quantum levels with increased
  shielding.
• H 1s1
• Li ..2s1
• Na ......3s1
• K ..4s1

40
Atomic radius trends

• Atomic radius decreases across a period of
  representative elements
• Valence shell (PEL) remains the same across a
  period, same shielding across the
  periodhowever
• The protons increases across a period
• The increased nuclear charge pulls shells
  closer to the nucleus

41
Atomic Radius

• Consider the 2nd periodfilling n 2
• Li Be B C N O F Ne
• p 3 4 5 6 7 8 9 10
• ? decreasing atomic radius

42
Atomic radius

• Atomic radius remains same across a row of
  transition metals
• Why?

43
Ionization Energy

• Ionization Energy energy needed to remove the
  highest energy electron from an atom in its
  gaseous state.
• See page 272/273, IE gt 0
• Na(g) ? Na (g) e IE1 495
  kJ/mole

44
IE Trends

• First IE (IE1 ) becomes less endothermic (less )
  down a group
• See table 7.5 on page 272
• Why?
• As you go down a group, the electron being
  removed is farther from the nucleus and shielded
  by more core electrons from the attractive forces
  of the nucleus.
• Therefore, its easier to remove.

45
IE Trends

• In general, first IE (IE1 )increases across a
  period.
• See figure 7.31 on page 273
• Why?
• Atoms become smaller across a period and the
  core electrons (shielding) remains the same while
  nuclear charge increases.
• Electron to be removed is held more tightly to
  the nucleus across a period.

46
Exceptions to IE Trends

• A dip in IE1 is observed for elements in group 3A
  and 6A.
• 3A elements are all ns2p1
• Hypothesized that the s2 electrons shield the
  first p electron
• 6A elements are all ns2p4
• Hypothesized that the first pairing of p
  electrons increases repulsions and thus this
  electron is easier to remove.

47
Trends in Successive IE

• IE increases as additional electrons are removed
  from a given element
• see table 7.5 on page 272
• Na(g) ? Na (g) e IE1 495
  kJ/mole
• Na (g) ? ____ e IE2 4560
  kJ/mol

48
Trends in Successive IE

• IE jumps when the first core electron is removed.
• Why?
• Na(g) ? Na (g) e IE1 495
  kJ/mole (val. e)
• Na (g) ? ____ e IE2 4560
  kj/mol (core e)

49
Electron Affinity

• EA energy change associated with the addition
  of an electron to a gaseous atom.
• In this text, EA lt 0 (convention varies)
• See page 275
• X (g) e ? X-(g)

50
EA Trends

• MANY EXCEPTIONS!
• In general, EA becomes less negative down a
  group.
• In general, EA becomes more negative across a
  period.

51
Periodic Trends

• Atomic radius
• Ionization Energy (gt0)
• First IE and successive IE
• 3A and 6A exceptions
• Electron Affinity (lt0)